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{\bf Bridget Eileen Tenner}
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{\bf Tiling Parity Results and the Holey Square Solution}
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We prove combinatorially that the parity of the number of domino
tilings of a region is equal to the parity of the number of domino
tilings of a particular subregion. Using this result we can resolve
the holey square conjecture.  We furthermore give combinatorial proofs
of several other tiling parity results, including that the number of
domino tilings of a particular family of rectangles is always odd.

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